An oscillation model of a single free piston engine generator which is coupled with a linear generator is presented in this paper. Based on the dynamics and energy equilibrium, the oscillation model is described by the mass spring damping system. It demonstrates that the generator could be regarded as a single freedom self-exited vibration system. The excitation is the periodical combustion in the cylinder. And the system reaches a limit loop after several cycles. The frequency and amplitude characteristics with the effects of key variables are shown. It provides a power map as function of the stiffness and mass, which will be applied into the match design and optimization.